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utcminusfour said..
I think required board width needs much more study in general. For instance a common statement is that tail width is needed to create leverage over the foil. Another common statement is that with larger sails you need more tail width. Is the width needed for the foil or the sail? Further, what sail attributes effect this balance? How does sail aspect ratio, location of the sails draft, and foil design all contribute the required tail width. My gut tells me it is related to the down force created by the sail. I am searching for the sweet spot in freeride gear where the smallest kit both in size and quantity covers 5-35 knots. This probably deserves a new thread.
I was hoping one of the more experienced racers would chime in...
Width, imho, is more related to where the apparent wind is and what you are trying to do with the foil (and what it's trying to do to you

).
Short version: board width is much more related to how far forward the apparent wind is and how much side force on the foil mast you are trying to generate. This is very dependent on what points of sail you are trying to optimize for. The easiest way to see this is upwind/downwind racing boards sailed out on the rail going upwind and can easily be sailed with the back foot inboard downwind (chicken straps). Freeride boards don't worry about this because they aren't worried about the last 5-10 degrees of upwind performance. Also, see the Patrik video where he talks about the 2020 lineup. The Foil Slalom boards have more pinched tails because they aren't required to go upwind.
Ditto on the leverage issue. It's in forward apparent wind scenarios where the foil mast has the most side force on it that width helps you counter. Also, if you are trying to heel the entire board/rig over to windward, the further you are out on the rail and the wider that rail is, the easier it is.
In terms of studies, we have empirical testing. Wider boards (100cm) seem to go windward better than narrower boards (91cm) as seen at the Formula Worlds. Similarly, in slalom situations, board width doesn't seem to be a primary factor.
Sail weight/downforce is trimmed fore/aft with mast base/foot strap/foot position. Easiest way to see is in light wind going windward, a lot of racers will put the back foot in front of the back strap since there's less sail downforce - but it's still on the rail.
For the moment, I'm ignoring practical considerations such as how do I cram in 150-170 l for the bigger guys in something that's only 225cm long and not make it too thick. If I make the board wider, it's easier - plus the added benefit that the board is more stable. But that's a different design consideration.